Edge incident 2-edge coloring of graphs

Abstract

The edge incident 2-edge coloring of a graph [Formula: see text] is an edge coloring of the graph [Formula: see text] such that not more than two colors are assigned to the edges incident to an edge [Formula: see text] in [Formula: see text]. In other words, for every edge [Formula: see text] in [Formula: see text], the edge [Formula: see text] and all the edges that are incident to the edge [Formula: see text] is in at most two different color classes. The edge incident 2-edge coloring number [Formula: see text] is the maximum number of colors in any edge incident 2-edge coloring of [Formula: see text]. The main objective of this paper is to study the edge incident 2-edge coloring concept and apply the same to some graph classes. Besides finding the exact values of these parameters, we also obtain some bounds.